The Taylor Pipe Flow experiment was designed to be a continuation of the research on the dispersion of soluble matter through a tube conducted by G.I. Taylor  . In two-dimensional channel models and three-dimensional circular- and square-faced model glass pipes, we explore the theory of Taylor dispersion explaining the motion of a passive scalar transported by laminar flow. Studies here at the University of North Carolina in Chapel Hill are implemented to better understand the stochastic system of the dispersion, primarily by calculating the first three moments of the advection of the solute. Depending on the characteristic length and mean velocity, we observe the effects of Poiseuille flow as either advection or diffusion dominates at different regimes characterized by the Taylor time scale, t = R2/D. We conduct experiments to better understand the regimes characterized by the dimensionless Péclet number, Pe = UR/D, where R is the pipe radius, U is the velocity, and D is the diffusion coefficient of the solute. In experiments, we take the intensity of a fluorescein-dyed portion of distilled water and find its corresponding concentration by solving an inverse problem of intensity to concentration. This serves as results to compare with the theoretical approach.